Every so often I have an epiphany about life or about teaching, and even less frequently I have one that lies in the intersection of the two. I realized recently that my OCD, type-A, control freak nature (while often productive and even, some say, endearing) has just as much an effect on my classroom as it does on my life outside of school. Although it would be healthy for me to take a step back and learn to relinquish a little control in both realms, I'll spare you the details of my personal life and stick to my teaching. This "relinquishing of control" is something I'll call the "33-50-95-100% Model".

I'll start off by explaining the model I had been using, which I'll call the "100% Model." In the 100% model, I'd introduce a new concept, design a class period or maybe two of very thoughtful, methodical guided practice, assess the objective on an Exit Ticket, and foolishly hope that 100% of students had mastered the topic. Undoubtedly they wouldn't, and so I'd hurriedly try to patch the holes using Do Now's or spiral homework assignments over the next couple of weeks, so that all 100% would at least master the objective by the time of the unit test. Which, of course, they wouldn't.

Right now my Precalculus class is finishing up their last unit, on limits & continuity. The first topic in that unit was reading the graph of a piecewise function to determine one- and two-sided limits, function values, and types of discontinuities at certain points. And, as with anything graph-related, there was a group of students (about one-third of the class) who immediately caught on (aced that day's exit ticket) while the rest seemed to have forgotten everything they ever knew about reading a graph. Ordinarily I would have done a significant amount of spiral review, but due to timing constraints I had to give a quiz prematurely. Of course, the 33% who understood the material aced the quiz, and the 67% who didn't, didn't.

I had a little more wiggle room during the week after the quiz, so when I handed back the quizzes I did so in groups of 3, basically putting one of the stronger students in charge of tutoring 1-2 peers who were struggling. They had 30 minutes to figure out their mistakes on the quiz and then complete a practice sheet with similar problems. At the end of the period there was an independent exit ticket, again with similar problems. Results of the exit ticket suggest that around 50% have mastered the content, while all but a few are on their way and much closer to mastering it than they were at the time of the quiz.

I suspect that spiral review (through Do Nows, quick drills, etc.) will be much more effective now that a critical mass of students have mastered the objective - hopefully so much so that by the time of the unit test, only a few students will still be struggling. And those are precisely the students that I will be able to focus my attention on during after school tutorials.

I think the only real difference between the two models is that in the 100% model I was operating on the (obviously false) premise that if I just taught a particular topic "well enough" the first time, all students would be able to master it at the level I required and on a timetable that was convenient for me. The latter model is simply acknowledging the unreasonableness of this assumption by allowing kids to move on with a slightly new topic so that they don't feel like they're beating a dead horse every time they walk into class, and then coming back to the original topic in a few days or weeks with a fresh set of eyes and a built-in set of peer tutors. The buzz in the classroom was focused and productive during the peer tutoring session; the strong students were challenged to explain problems and forced to ask questions about the subtler points that even they struggled with, while the weaker students got the one-on-one targeted instruction that they needed but would have never gotten in a large group review.

Of course, this was not easy for me. I had to accept that 100%-or-Bust only has one possible outcome, and I had to trust both my student tutors and tutees to do what they needed to do while I merely facilitated or clarified a point here or there. But at the end of the day, I think I have myself a new paradigm for thinking about how my students actually learn (as opposed to how I wanted them to learn).